In recent years, radiotherapy has experienced a profound reduction in delivery times and improvement in plan quality with the establishment of dynamic gantry treatments such as Volumetric Modulated Arc Therapy (VMAT) [Otto, 2008, Yu, 1995]. The success of VMAT has no doubt motivated a substantial wave of research in furthering dynamic delivery capabilities of medical accelerator in routine treatment.
A natural progression beyond VMAT has led to increasing modulation capabilities and improved dose gradient formation through inclusion of dynamic collimator angle optimization such as in the work by Zhang et al. (2010), and in the work by Yang et al. (2011) who investigated the possibility of incorporating dynamic couch angle optimization to form a set of optimized arc trajectories. The concept of combining gantry rotation with a rotation of the patient couch was in fact first proposed by Podgorsak et al. (1988) for stereotactic brain treatment, to deliver a continuous single gantry arc with dynamic couch rotation so as to avoid producing opposed beam pairs. Complex for the time, the technique was not widely adopted into mainstream clinical use, possibly due to the risk associated with accurately administering a highly dynamic treatment without sufficient safety and verification technologies.
To define optimal couch-gantry angles, Pugachev and Xing (2001) developed the concept of Beam's Eye View Dose (BEVd), from which a score can be calculated from each BEV by evaluating normal tissue dose relative to well accepted tissue tolerances [Marks, 2010]. The approach was used in Intensity Modulated Radiation Therapy (IMRT) for beam angle optimization and later was implemented as a couch-gantry angle scoring method in arc therapy [Ma et al., 2009], Trajectory Modulated Arc Therapy (TMAT) optimization by Fahimian et al. (2013) and recently implemented in the Station Parameter Optimization in Radiotherapy (SPORT) algorithm by Kim et al. (2015).
Investigating the potential benefits of using radiation beams incident from all possible directions, Dong et al. (2013a, 2013b), performed a series of treatment plan optimizations starting with 1162 static beams with 6 degree separation spanning 4π solid angle. Dong et al. demonstrated substantially improved plan quality over coplanar VMAT plans using a method to select and optimize fluence from a high scoring subset of 14-22 of the 1162 static fields.
Smyth et al. (2013) developed another dynamic couch VMAT optimization method in which graph optimization is used to optimally traverse the deliverable gantry-couch space with graph nodes representing cost from the incident angle. The results demonstrated a modest improvement over coplanar VMAT for several treatment sites.
In 2015, 3 separate research groups made efforts toward trajectory optimization. MacDonald and Thomas (2015) implemented a geometrical BEV analysis to score incident angles using QUANTEC dose limits [Marks, 2010] and subsequently determined optimal trajectories based on a score map. Papp et al. (2015) developed a non-coplanar VMAT approach in which they first determine a set of high-scoring incident beams using a beam angle optimization and then connect the incident angles using a travelling salesman minimization approach. Wild et al. (2015) also implemented an approach of identifying high scoring incident angles and connecting the angles with a travelling salesman approach. Wild et al. also compared the dosimetric capabilities of many forms of coplanar and non-coplanar trajectory possibilities to a 4π static field IMRT plan consisting of 1374 incident IMRT beams. The set of 4π static field IMRT plans were found to produce a best overall baseline for a dosimetric comparison of the trajectory techniques and the travelling salesman approach was found to be a good choice when considering treatment delivery times.
It can be shown that all of the published trajectory optimization algorithms developed to date share the following common core approach, illustrated in FIGS. 1A-B: First, an incident beam angle scoring function is defined and used to map out the “goodness” of incident beam angles. The gantry-couch angle score map 100 in the figures show the score assigned to each gantry-couch angle pair, where lighter shading indicates higher score and darker shading indicates lower score; Second, collision zones 102, 104 are marked out for avoidance and then an optimization is performed to determine optimal trajectories 106 from the gantry-couch angle score map by linking or traversing the “goodness” map, avoiding the collision zones for the delivery device. Squares 108 and 110 in FIG. 1B represent the beam's eye view from points A and B on trajectory T. Oval 112 is a single region to treat at point A, and ovals 114 and 116 are two disconnected regions to treat at point B.
Using this common approach, a fundamental loss of information occurs: The connectedness of ideal regions to treat, from one incident angle to the next, is entirely lost. By using only a single calculated score for each incident beam angle, the geometrical relationship of adjacent apertures is not preserved and the deliverable trajectories ultimately degrade from inadequate dynamic multi-leaf collimator (MLC) delivery capabilities and MLC aperture forming contention issues. Consequently, the resulting trajectories cannot be considered optimal using any of the approaches summarized above.
A consequence of not considering the geometrical relationship of apertures forming a trajectory is further illustrated by considering the progressive resolution VMAT optimization example of a hollow cylindrical target 200 surrounding an organ at risk, as shown in FIGS. 2A-C. By cylindrical symmetry, all axial, coplanar incident beam angles can be shown to score equal “goodness”. This target/avoidance geometry was constructed specifically to present 2 geometrically separate choices for each MLC leaf pair from every angle (MLC aperture contention).
To maximally shield the central organ at risk and treat the target, human intuition would find it logical to arrange a set of MLC leaf pairs 202, 204 to expose only one side 206 of the hollow cylinder and not traverse across the central avoidance for the entire duration of the trajectory such as in FIG. 2A. Yet, in this example, such a solution is probabilistically undiscoverable without some mathematical consideration of MLC synchronization. In FIG. 2B, a “confused” trajectory is illustrated with the confusion stemming from a lack of MLC aperture synchronization between the earliest/coarsest sampling stages of VMAT. In FIG. 2C, a second “confused” MLC is illustrated with the confusion stemming from a lack of MLC synchronization amongst the MLC leaf pairs of a given aperture. It is important to note that the aperture score is identical in each case.